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Per Enflo 《Acta Mathematica》1987,158(1):213-313
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In 1996 P. Enflo introduced the concept of extremal vectors and their connection to the Invariant Subspace Problem. The study of backward minimal vectors gives a new method of finding invariant subspaces which is more constructive than the previously known methods. In this article we study the properties and behaviour of extremal vectors, give some new formulas related to backward minimal vectors and improve results from papers by Ansari and Enflo (1998) and Enflo (1998).
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Enflo BO Hedberg CM Rudenko OV 《The Journal of the Acoustical Society of America》2005,117(2):601-612
Simplified nonlinear evolution equations describing non-steady-state forced vibrations in an acoustic resonator having one closed end and the other end periodically oscillating are derived. An approach based on a nonlinear functional equation is used. The nonlinear Q-factor and the nonlinear frequency response of the resonator are calculated for steady-state oscillations of both inviscid and dissipative media. The general expression for the mean intensity of the acoustic wave in terms of the characteristic value of a Mathieu function is derived. The process of development of a standing wave is described analytically on the base of exact nonlinear solutions for different laws of periodic motion of the wall. For harmonic excitation the wave profiles are described by Mathieu functions, and their mean energy characteristics by the corresponding eigenvalues. The sawtooth-shaped motion of the boundary leads to a similar process of evolution of the profile, but the solution has a very simple form. Some possibilities to enhance the Q-factor of a nonlinear system by suppression of nonlinear energy losses are discussed. 相似文献
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P. Enflo 《Israel Journal of Mathematics》1970,8(3):230-252
Topological groups which are free from small subgroups and topological groups with locally uniformly continuous group multiplication
are considered. Results concerning square roots, one-parameter subgroups and extensions of local groups are obtained as well
as some generalisations of theorems for locally compact groups. 相似文献
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It is proved that Lp(μ) does not have an unconditional basis if the cardinality of Lp(μ) is sufficiently large and μ is a finite measure. It is also shown that Lp(μ) has a weaker kind of basis for arbitrary μ and 1 < p < ∞. A new truncation lemma concerning sequences in Lp equivalent to the usual lp-basis is given. This lemma is used in solving the problem of when lp(Γ) imbeds in Lr(μ) for uncountable sets Γ and finite measures μ. It may also be used to give a nonprobabilistic proof of the fact (due to Schwartz-Kwapien) that there exist non-q-absolutely summing operators from L∞to Lqfor 2 < q < ∞. It is again used in proving that basic sequences in Lp equivalent to the usual lp-basis admit subsequences with a complemented linear span. Other applications of the techniques introduced are also given. 相似文献
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For a bounded linear operator on Hilbert space we define a sequence of so-called minimal vectors in connection with invariant subspaces and show that this presents a new approach to invariant subspaces. In particular, we show that for any compact operator some weak limit of the sequence of minimal vectors is noncyclic for all operators commuting with and that for any normal operator , the norm limit of the sequence of minimal vectors is noncyclic for all operators commuting with . Thus, we give a new and more constructive proof of existence of invariant subspaces. The sequence of minimal vectors does not seem to converge in norm for an arbitrary bounded linear operator. We will prove that if belongs to a certain class of operators, then the sequence of such vectors converges in norm, and that if belongs to a subclass of , then the norm limit is cyclic.